The shifts in the four-body recombination peaks, due to an effective range correction to the zero-range model close to the unitary limit, are obtained and used to extract the corresponding effective range of a given atomic system. The approach is applied to an ultracold gas of cesium atoms close to broad Feshbach resonances, where deviations of experimental values from universal model predictions are associated with effective range corrections. The effective range correction is extracted with a weighted average given by $3.9\ifmmode\pm\else\textpm\fi{}0.8{R}_{\mathrm{vdW}}$, where ${R}_{\mathrm{vdW}}$ is the van der Waals length scale, which is consistent with the van der Waals potential tail for the Cs ${}_{2}$ system. The method can be generally applied to other cold atom experimental setups to determine the contribution of the effective range to the tetramer dissociation position.The shifts in the four-body recombination peaks, due to an effective range correction to the zero-range model close to the unitary limit, are obtained and used to extract the corresponding effective range of a given atomic system. The approach is applied to an ultracold gas of cesium atoms close to broad Feshbach resonances, where deviations of experimental values from universal model predictions are associated with effective range corrections. The effective range correction is extracted with a weighted average given by $3.9\ifmmode\pm\else\textpm\fi{}0.8{R}_{\mathrm{vdW}}$, where ${R}_{\mathrm{vdW}}$ is the van der Waals length scale, which is consistent with the van der Waals potential tail for the Cs${}_{2}$ system. The method can be generally applied to other cold atom experimental setups to determine the contribution of the effective range to the tetramer dissociation position.

arXiv:1211.2270Physical Review AJan 17, 201312 citations

Binding and structure of tetramers in the scaling limit

M. R. Hadizadeh, Marcelo Takeshi Yamashita, Lauro Tomio +2 more

The momentum-space structure of the Faddeev-Yakubovsky (FY) components of weakly bound tetramers is investigated at the unitary limit using a renormalized zero-range two-body interaction. The results, obtained by considering a given trimer level with binding energy ${B}_{3}$ , provide further support to a universal scaling function relating the binding energies of two successive tetramer states. The correlated scaling between the tetramer energies comes from the sensitivity of the four-boson system to a short-range four-body scale. Each excited $N$ th tetramer energy ${B}_{4}^{(N)}$ moves as the short-range four-body scale changes, while the trimer properties are kept fixed, with the next excited tetramer ${B}_{4}^{(N+1)}$ emerging from the atom-trimer threshold for a universal ratio ${B}_{4}^{(N)}/{B}_{3}={B}_{4}^{(N)}/{B}_{4}^{(N+1)}\ensuremath{\simeq}4.6$, which does not depend on $N$ . We show that both channels of the FY decomposition [atom-trimer ( $K$ type) and dimer-dimer ( $H$ type)] present high-momentum tails that reflect the short-range four-body scale. We also found that the $H$ channel is favored over the $K$ channel at low momentum, when the four-body momentum scale largely overcomes the three-body scale.The momentum-space structure of the Faddeev-Yakubovsky (FY) components of weakly bound tetramers is investigated at the unitary limit using a renormalized zero-range two-body interaction. The results, obtained by considering a given trimer level with binding energy ${B}_{3}$, provide further support to a universal scaling function relating the binding energies of two successive tetramer states. The correlated scaling between the tetramer energies comes from the sensitivity of the four-boson system to a short-range four-body scale. Each excited $N$th tetramer energy ${B}_{4}^{(N)}$ moves as the short-range four-body scale changes, while the trimer properties are kept fixed, with the next excited tetramer ${B}_{4}^{(N+1)}$ emerging from the atom-trimer threshold for a universal ratio ${B}_{4}^{(N)}/{B}_{3}={B}_{4}^{(N)}/{B}_{4}^{(N+1)}\ensuremath{\simeq}4.6$, which does not depend on $N$. We show that both channels of the FY decomposition [atom-trimer ($K$ type) and dimer-dimer ($H$ type)] present high-momentum tails that reflect the short-range four-body scale. We also found that the $H$ channel is favored over the $K$ channel at low momentum, when the four-body momentum scale largely overcomes the three-body scale.

arXiv:1110.5214Physical Review AFeb 8, 201233 citations

Significance of Classically Forbidden Transitions

WORLD SCIENTIFIC eBooksSep 26, 20190 citations

Molecular properties

Qiming Sun

Theoretical and computational chemistryJan 1, 20251 citation

Universality and scaling limit of weakly-bound tetramers

M. R. Hadizadeh, Marcelo Takeshi Yamashita, Lauro Tomio +2 more

The occurrence of a new limit cycle in few-body physics, expressing a universal scaling function relating the binding energies of two successive tetramer states, is revealed by considering a renormalized zero-range two-body interaction in bound state of four identical bosons. The tetramer energy spectrum is obtained by adding a boson to an Efimov bound state with energy B3 in the unitary limit (for zero two-body binding energy or infinite two-body scattering length). Each excited Nth tetramer energy B(N)4 is shown to slide along a scaling function as a short-range four-body scale is changed, emerging from the 3+1 threshold for a universal ratio B4(N)/B3 = 4.6, which does not depend on N. The new scale can also be revealed by a resonance in the atom-trimer recombination process.The occurrence of a new limit cycle in few-body physics, expressing a universal scaling function relating the binding energies of two successive tetramer states, is revealed by considering a renormalized zero-range two-body interaction in bound state of four identical bosons. The tetramer energy spectrum is obtained by adding a boson to an Efimov bound state with energy B3 in the unitary limit (for zero two-body binding energy or infinite two-body scattering length). Each excited Nth tetramer energy B(N)4 is shown to slide along a scaling function as a short-range four-body scale is changed, emerging from the 3+1 threshold for a universal ratio B4(N)/B3 = 4.6, which does not depend on N. The new scale can also be revealed by a resonance in the atom-trimer recombination process.

AIP conference proceedingsJan 1, 20126 citations

{R}_{\mathrm{vdW}}

is the van der Waals length scale, which is consistent with the van der Waals potential tail for the Cs

{}_{2}

system. The method can be generally applied to other cold atom experimental setups to determine the contribution of the effective range to the tetramer dissociation position.

{B}_{3}

, provide further support to a universal scaling function relating the binding energies of two successive tetramer states. The correlated scaling between the tetramer energies comes from the sensitivity of the four-boson system to a short-range four-body scale. Each excited

N

th tetramer energy

{B}_{4}^{(N)}

moves as the short-range four-body scale changes, while the trimer properties are kept fixed, with the next excited tetramer

{B}_{4}^{(N+1)}

emerging from the atom-trimer threshold for a universal ratio ${B}_{4}^{(N)}/{B}_{3}={B}_{4}^{(N)}/{B}_{4}^{(N+1)}\ensuremath{\simeq}4.6$, which does not depend on

N

. We show that both channels of the FY decomposition [atom-trimer (

K

type) and dimer-dimer (

H

type)] present high-momentum tails that reflect the short-range four-body scale. We also found that the

H

channel is favored over the

K

channel at low momentum, when the four-body momentum scale largely overcomes the three-body scale.